Amarkovian approach to the mathematical thesis pdf

Andrei Kolmogorov developed in a 1931 paper a large part of the early theory of continuous-time Markov processes. [45] [46] Kolmogorov was partly inspired by Louis Bachelier's 1900 work on fluctuations in the stock market as well as Norbert Wiener 's work on Einstein's model of Brownian movement. [45] [47] He introduced and studied a particular set of Markov processes known as diffusion processes, where he derived a set of differential equations describing the processes. [45] [48] Independent of Kolmgorov's work, Sydney Chapman derived in a 1928 paper an equation, now called the Chapman–Kolmogorov equation , in a less mathematically rigorous way than Kolmogorov, while studying Brownian movement. [49] The differential equations are now called the Kolmogorov equations [50] or the Kolmogorov–Chapman equations. [51] Other mathematicians who contributed significantly to the foundations of Markov processes include William Feller , starting in 1930s, and then later Eugene Dynkin , starting in the 1950s. [46]